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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>Thus, rewrite the differential equation in s-domain:</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\begin{aligned}
-[2sY(s)+s^2Y'(s)-y(0)]+[Y(s)+sY'(s)]+Y(s) &amp;=&amp; \frac{2}{s}\\
(-s^2+s)Y'(s)+2(1-s)Y(s) &amp;=&amp; \frac{2-2s}{s}\\
Y'(s)+\frac{2}{x}Y(s) &amp;=&amp; \frac{2}{s^2}.\\
Y(s)  &amp;=&amp; \frac{2}{s}+\frac{c}{s^2},\quad c\in\mathbb{R}
\end{aligned}
\end{equation*}
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<p class="continuation">The inverse transform gives</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
y(t)=2+ct.
\end{equation*}
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<p class="continuation">Match with the second initial condition which we haven’t used yet, the solution to this IVP is</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
y(t) = 2-4t.
\end{equation*}
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<span class="incontext"><a href="sec8_4.html#p-479" class="internal">in-context</a></span>
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